The Sensitivity of the Advanced LIGO Detectors at the Beginning of GravitationalWave Astronomy

D. V. Martynov,1 E. D. Hall,1 B. P. Abbott,1 R. Abbott,1 T. D. Abbott,2 C. Adams,3 R. X. Adhikari,1

R. A. Anderson,1 S. B. Anderson,1 K. Arai,1 M. A. Arain,4 S. M. Aston,3 L. Austin,1 S. W. Ballmer,5 M. Barbet,4

D. Barker,6 B. Barr,7 L. Barsotti,8 J. Bartlett,6 M. A. Barton,6 I. Bartos,9 J. C. Batch,6 A. S. Bell,7 I. Belopolski,9

J. Bergman,6 J. Betzwieser,3 G. Billingsley,1 J. Birch,3 S. Biscans,8 C. Biwer,5 E. Black,1 C. D. Blair,10C. Bogan,11

C. Bond,34,36 R. Bork,1 D. O. Bridges,3 A. F. Brooks,1 D. D. Brown,34,22 L. Carbone,34 C. Celerier,12 G. Ciani,4

F. Clara,6 D. Cook,6 S. T. Countryman,9 M. J. Cowart,3 D. C. Coyne,1 A. Cumming,7 L. Cunningham,7

M. Damjanic,11 R. Dannenberg,1 K. Danzmann,13,11 C. F. Da Silva Costa,4 E. J. Daw,14 D. DeBra,12 R. T. DeRosa,3

R. DeSalvo,15 K. L. Dooley,16 S. Doravari,3 J. C. Driggers,6 S. E. Dwyer,6 A. Effler,3 T. Etzel,1 M. Evans,8

T. M. Evans,3 M. Factourovich,9 H. Fair,5 D. Feldbaum,4,3 R. P. Fisher,5 S. Foley,8 M. Frede,11 A. Freise,34

P. Fritschel,8 V. V. Frolov,3 P. Fulda,4 M. Fyffe,3 V. Galdi,15 J. A. Giaime,2,3 K. D. Giardina,3 J. R. Gleason,4

R. Goetz,4 S. Gras,8 C. Gray,6 R. J. S. Greenhalgh,17 H. Grote,11 C. J. Guido,3 K. E. Gushwa,1 E. K. Gustafson,1

R. Gustafson,18 G. Hammond,7 J. Hanks,6 J. Hanson,3 T. Hardwick,2G. M. Harry,19 K. Haughian,7 J. Heefner∗,1

M. C. Heintze,3 A. W. Heptonstall,1 D. Hoak,20 J. Hough,7 A. Ivanov,1 K. Izumi,6 M. Jacobson,1 E. James,1

R. Jones,7 S. Kandhasamy,16 S. Karki,21 M. Kasprzack,2 S. Kaufer,13 K. Kawabe,6 W. Kells,1 N. Kijbunchoo,6

E. J. King,22 P. J. King,6 D. L. Kinzel,3 J. S. Kissel,6 K. Kokeyama,2 W. Z. Korth,,1 G. Kuehn,11 P. Kwee,8

M. Landry,6 B. Lantz,12 A. Le Roux,3 B. M. Levine,6 J. B. Lewis,1 V. Lhuillier,6 N. A. Lockerbie,23 M. Lormand,3

M. J. Lubinski,6 A. P. Lundgren,11 T. MacDonald,12 M. MacInnis,8 D. M. Macleod,2 M. Mageswaran,1

K. Mailand,1 S. Marka,9 Z. Marka,9 A. S. Markosyan,12 E. Maros,1 I. W. Martin,7 R. M. Martin,4 J. N. Marx,1

K. Mason,8 T. J. Massinger,5 F. Matichard,8 N. Mavalvala,8 R. McCarthy,6 D. E. McClelland,24 S. McCormick,3

G. McIntyre,1 J. McIver,1 E. L. Merilh,6 M. S. Meyer,3 P. M. Meyers,25 J. Miller,8 R. Mittleman,8 G. Moreno,6

C. L. Mueller,4 G. Mueller,4 A. Mullavey,3 J. Munch,22 P. G. Murray,7 L. K. Nuttall,5 J. Oberling,6 J. O’Dell,17

P. Oppermann,11 Richard J. Oram,3 B. O’Reilly,3 C. Osthelder,1 D. J. Ottaway,22 H. Overmier,3 J. R. Palamos,21

H. R. Paris,12 W. Parker,3 Z. Patrick,12 A. Pele,3 S. Penn,26 M. Phelps,7 M. Pickenpack,11V. Piero,15 I. Pinto,15

J. Poeld,11 M. Principe,15 L. Prokhorov,27 O. Puncken,11 V. Quetschke,28 E. A. Quintero,1 F. J. Raab,6

H. Radkins,6 P. Raffai,29 C. R. Ramet,3 C. M. Reed,6 S. Reid,30 D. H. Reitze,1,4 N. A. Robertson,1,7 J. G. Rollins,1

V. J. Roma,21 J. H. Romie,3 S. Rowan,7 K. Ryan,6 T. Sadecki,6 E. J. Sanchez,1 V. Sandberg,6 V. Sannibale,1

R. L. Savage,6 R. M. S. Schofield,21 B. Schultz,11 P. Schwinberg,6 D. Sellers,3 A. Sevigny,6 D. A. Shaddock,24

Z. Shao,1 B. Shapiro,12 P. Shawhan,31 D. H. Shoemaker,8 D. Sigg,6 B. J. J. Slagmolen,24 J. R. Smith,32

M. R. Smith,1 N. D. Smith-Lefebvre,1 B. Sorazu,7 A. Staley,9 A. J. Stein,8 A. Stochino,1 K. A. Strain,7 R. Taylor,1

M. Thomas,3 P. Thomas,6 K. A. Thorne,3 E. Thrane,33 K. V. Tokmakov,7,37 C. I. Torrie,1 G. Traylor,3 G. Vajente,1

G. Valdes,28 A. A. van Veggel,7 M. Vargas,3 A. Vecchio,34 P. J. Veitch,22 K. Venkateswara,35 T. Vo,5 C. Vorvick,6

S. J. Waldman,8 M. Walker,2 R. L. Ward,24 J. Warner,6 B. Weaver,6 R. Weiss,8 T. Welborn,3 P. Weßels,11

C. Wilkinson,6 P. A. Willems,1 L. Williams,4 B. Willke,13,11 I. Wilmut,17 L. Winkelmann,11 C. C. Wipf,1

J. Worden,6 G. Wu,3 H. Yamamoto,1 C. C. Yancey,31 H. Yu,8 L. Zhang,1 M. E. Zucker,1,8 and J. Zweizig1

1LIGO, California Institute of Technology, Pasadena, CA 91125, USA2Louisiana State University, Baton Rouge, LA 70803, USA3LIGO Livingston Observatory, Livingston, LA 70754, USA

4University of Florida, Gainesville, FL 32611, USA5Syracuse University, Syracuse, NY 13244, USA

6LIGO Hanford Observatory, Richland, WA 99352, USA7SUPA, University of Glasgow, Glasgow G12 8QQ, United Kingdom

8LIGO, Massachusetts Institute of Technology, Cambridge, MA 02139, USA9Columbia University, New York, NY 10027, USA

10University of Western Australia, Crawley, Western Australia 6009, Australia11Albert-Einstein-Institut, Max-Planck-Institut fur Gravitationsphysik, D-30167 Hannover, Germany

12Stanford University, Stanford, CA 94305, USA13Leibniz Universitat Hannover, D-30167 Hannover, Germany

14The University of Sheffield, Sheffield S10 2TN, United Kingdom15University of Sannio at Benevento, I-82100 Benevento,Italy and INFN, Sezione di Napoli, I-80100 Napoli, Italy

16The University of Mississippi, University, MS 38677, USA17Rutherford Appleton Laboratory, HSIC, Chilton, Didcot, Oxon OX11 0QX, United Kingdom

18University of Michigan, Ann Arbor, MI 48109, USA

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19American University, Washington, D.C. 20016, USA20University of Massachusetts-Amherst, Amherst, MA 01003, USA

21University of Oregon, Eugene, OR 97403, USA22University of Adelaide, Adelaide, South Australia 5005, Australia

23SUPA, University of Strathclyde, Glasgow G1 1XQ, United Kingdom24Australian National University, Canberra, Australian Capital Territory 0200, Australia

25University of Minnesota, Minneapolis, MN 55455, USA26Hobart and William Smith Colleges, Geneva, NY 14456, USA

27Faculty of Physics, Lomonosov Moscow State University, Moscow 119991, Russia28The University of Texas Rio Grande Valley, Brownsville, TX 78520, USA

29MTA Eotvos University, “Lendulet” Astrophysics Research Group, Budapest 1117, Hungary30SUPA, University of the West of Scotland, Paisley PA1 2BE, United Kingdom

31University of Maryland, College Park, MD 20742, USA32California State University Fullerton, Fullerton, CA 92831, USA

33Monash University, Victoria 3800, Australia34University of Birmingham, Birmingham B15 2TT, United Kingdom

35University of Washington, Seattle, WA 98195, USA(Dated: February 13, 2018)

The Laser Interferometer Gravitational Wave Observatory (LIGO) consists of two widely sepa-rated 4 km laser interferometers designed to detect gravitational waves from distant astrophysicalsources in the frequency range from 10 Hz to 10 kHz. The first observation run of the AdvancedLIGO detectors started in September 2015 and ended in January 2016. A strain sensitivity of bet-ter than 10−23/

√Hz was achieved around 100 Hz. Understanding both the fundamental and the

technical noise sources was critical for increasing the astrophsyical strain sensitivity. The averagedistance at which coalescing binary black hole systems with individual masses of 30M could bedetected above a signal-to-noise ratio (SNR) of 8 was 1.3 Gpc, and the range for binary neutronstar inspirals was about 75 Mpc. With respect to the initial detectors, the observable volume of theUniverse increased by a factor 69 and 43, respectively. These improvements helped Advanced LIGOto detect the gravitational wave signal from the binary black hole coalescence, known as GW150914.

PACS numbers: 04.80.Nn, 95.55.Ym, 95.75.Kk, 07.60.Ly

I. INTRODUCTION

The possibility of using interferometers as gravitationalwave detectors was first considered in the early 1960s [1].In the 1970s and 1980s, long-baseline broadband laser in-terferometric detectors were proposed with the potentialfor an astrophysically interesting sensitivity [2, 3]. Overseveral decades, this vision evolved into a world-wide net-work of ground based interferometers [4–6]. These instru-ments target gravitational waves produced by compactbinary coalescences, supernovae, non-axisymmetric pul-sars, cosmological background as well as any unknownastrophysical sources in the audio frequency band, from10 Hz to 10 kHz [7].

The first generation of LIGO detectors consisted oftwo 4-km-long and one 2-km-long interferometers in theUnited States [10]: L1 in Livingston, Louisiana, H1 andH2 in Hanford, Washington. They were operationaluntil 2010 and reached their designed strain sensitiv-ity over the detection band, with a peak sensitivity of2 × 10−23/

√Hz at 200 Hz. Astrophysically relevant re-

sults were produced by the initial LIGO detectors [11–14], however, no gravitational wave signals were detected.

The second generation Advanced LIGO detectors [15]were installed in the existing facilities from 2010 to 2014.This new generation of instruments was designed to be10 times more sensitive than initial LIGO, and promised

to increase the volume of the observable universe by afactor of 1000. Commissioning of the newly−installed de-tectors took place from mid 2014 to mid 2015. In Septem-ber 2015, Advanced LIGO began the era of gravitationalwave astronomy with its first observation run (O1), col-lecting data until January 2016. This run has culminatedin the first direct detection of gravitational waves fromthe black hole coalescence, GW150914 [17, 18]. This sys-tem consisted of two black holes of about 35 solar masseach which merged about 500 Mpc away.

While the detectors were not yet operating at designsensitivity during the first observation run, their astro-physical reach was already significantly greater than thatof any previous detector in the frequency range 10 Hz–10 kHz. Around 100 Hz, the strain sensitivity was 8 ×10−24/

√Hz. For a system consisting of two 30M black

holes the sky location and source orientation-averagedrange was 1.3 Gpc, whereas for a binary neutron star sys-tem the range was 70–80 Mpc. This range is '4.1 and'3.5 times higher than that of the initial LIGO detec-tors, resulting in a factor of '70 and '40 improvement,respectively, of the volume that is probed and LIGO’sdetection potential.

In this paper we describe the noise characterizationof the Advanced LIGO detectors during the first obser-vation run. Sec. II introduces the optical configuration,control system and calibration of the detectors. Sec. IIIanalyzes the performance of the detectors and describes

3

all investigated noise sources. We end with the conclu-sions in Sec. IV.

Photodetectors

4 km

100 kW End test

massSignalRecycling

Mirror

Output Mode

Cleaner

BeamSplitterPower

Recycling Mirror

1064 nm

Input Mode

Cleaner

Laser

25W22W 800W

85mW

Input testmasses

End testmass

25mW

50/50 splitter

Electro-optic

modulator

9MHzoscillator

5

45MHz

L?

Lklk

l?

lpr

lsr

FIG. 1. Layout of an Advanced LIGO detector. The an-notations show the optical power in use during O1. Thesepower levels are a factor of '8 smaller compared to the de-signed power levels. The Nd:YAG laser [19], with wavelengthλ=1064 nm, is capable of producing up to 180 W, but only22 W were used. A suspended, triangular Fabry-Perot cav-ity serves as an input mode cleaner [20, 21] to clean up thespatial profile of the laser beam, suppress input beam jitter,clean polarization, and to help stabilize the laser frequency.The Michelson interferometer is enhanced by two 4-km-longresonant arm cavities, which increase the optical power in thearms by a factor of Garm ' 270. Since the Michelson interfer-ometer is operated near a dark fringe, all but a small fractionof the light is directed back towards the laser. The power re-cycling mirror resonates this light again to increase the powerincident on the beamsplitter by a factor of ' 40, improv-ing the shot noise sensing limit and filtering laser noises. Onthe antisymmetric side, the signal recycling mirror is used tobroaden the response of the detector beyond the linewidth ofthe arm cavities. An output mode cleaner is present at theantisymmetric port, to reject unwanted spatial and frequencycomponents of the light, before the signal is detected by themain photodetectors.

II. INTERFEROMETER CONFIGURATION

In general relativity, a gravitational wave far away fromthe source can be approximated as a linear disturbanceof the Minkowski metric, gµν = ηµν+hµν with the space-time deformation expressed as a dimensionless strain,hµν . In a Michelson interferometer we define the dif-ferential displacement as L = L‖−L⊥, where L‖ and L⊥are the lengths of the inline arm and the perpendiculararm, respectively, as shown in Fig. 1. With equal macro-scopic arm lengths, L0 ' L‖ ' L⊥, the gravitationalwave strain and the differential arm length are relatedthrough the simple equation L(f) = L‖ − L⊥ = h(f)L0,

102 103

Frequency, Hz

10-24

10-23

10-22

10-21

Str

ain

nois

e, 1

/Hz1/

2

Advanced LIGO, L1 (2015)Advanced LIGO, H1 (2015)

Enhanced LIGO (2010)Advanced LIGO design

FIG. 2. The strain sensitivity for the LIGO Livingston de-tector (L1) and the LIGO Hanford detector (H1) during O1.Also shown is the noise level for the Advanced LIGO design(gray curve) and the sensitivity during the final data collec-tion run (S6) of the initial detectors.

100 101 102 103

Observed chirp mass [M-]

101

102

103

104

105

Hor

izon

lum

inos

ity

dista

nce

[Mpc] Advanced LIGO design

Advanced LIGO, H1 (2015)Enhanced LIGO (2010)

FIG. 3. The sensitivity to coalescing compact binaries forthe Advanced LIGO design, first observation run (O1) andthe final run with the initial detectors (S6). The traces showthe horizon distance, which is the distance along the mostsensitive direction of the interferometer for a binary inspiralsystem that is seen head-on and for a signal-to-noise ratio of8. The horizontal axis is the chirp mass which is defined as

M = (1 + z)µ35M

25 , where M = M1 +M2 is the total mass,

µ = M1M2/M is the reduced mass, and z is the cosmologicalredshift. Units are in solar masses, M. The horizon distanceis computed for the case of equal masses M1 = M2 and usingthe inspiral–merger model from [22].

where h is the average differential strain induced intoboth arms at frequency f .

The test masses are four suspended mirrors that formFabry-Perot arm cavities. These mirrors can be consid-ered as inertial masses above the pendulum resonancefrequency (∼1 Hz). Any noise present in the differen-tial arm channel is indistinguishable from a gravitationalwave signal. Residual seismic noise, thermal noise asso-

4

ciated with the vertical suspension resonance, and thegravity-gradient background limits the useful frequencyrange to above 10 Hz as discussed in Sec. III A. Motion ofthe four test masses form the two most relevant degreesof freedom: differential and common arm lengths. Whilegravitational waves couple to the differential arm length,the common arm length is highly sensitive to changes inthe laser frequency according to the equation

L+(f) =L‖ + L⊥

2= L0

V (f)

ν, (1)

where ν = 2.82 × 1014 Hz is the laser carrier frequency,V (f) is the laser frequency noise. Signal L+ is used forfrequency stabilization of the main laser as discussed inSec. III E.

The central part of the interferometer is usually calledthe dual-recycled Michelson interferometer. Its functionis to optimize the detector’s response to gravitationalwaves. The power recycling cavity, formed by the powerrecycling mirror and the two input test masses, increasesoptical power incident on the arm cavities and passivelyfilters laser noises as discussed in Sec. III E. The signal re-cycling cavity, formed by the signal recycling mirror andthe two input test masses, is used to broaden the responseof the detector beyond the linewidth of the arm cavities.The Michelson interferometer, formed by the beam split-ter and the two input test masses, is controlled to keepthe antisymmetric port near the dark fringe. The dual re-cycled Michelson interferometer can thus be described bythree degrees of freedom: power recycling cavity lengthlp,+, signal recycling cavity length ls,+ and Michelsonlength l−, defined as

lp,+ = lpr +l‖ + l⊥

2

ls,+ = lsr +l‖ + l⊥

2l− = l‖ − l⊥,

(2)

where distances lpr, lsr, l‖ and l⊥ are defined in Fig. 1.The most important optical parameters of the Ad-

vanced LIGO interferometers are summarized in Table I.The beam size here is defined as the distance from thebeam center to the point when intensity is reduced by afactor 1/e2. The cavity pole fp determines the width ofthe cavity resonance and is given by

fp =Y c

8πL0, (3)

where c is the speed of light and Y 1 is the totaloptical loss in the cavity, including transmission of theinput and output cavity couplers as well as scatteringand absorption losses. The response of the AdvancedLIGO interferometers is diminished at high frequenciesdue to common and differential coupled cavity poles (f+and f−) according to the transfer functions

K+ =f+

if + f+; K− =

f−if + f−

. (4)

TABLE I. List of optical parameters

Parameter Value Unit

Laser wavelength 1064 nm

Arm cavity length, L0 3994.5 m

Power recycling cavity length, lp,+ 57.66 m

Signal recycling cavity length, ls,+ 56.01 m

Michelson asymmetry, l− 8 cm

Input mode cleaner length (round trip) 32.95 m

Output mode cleaner length (round trip) 1.13 m

Input mode cleaner finesse 500

Output mode cleaner finesse 390

Round trip loss in arm cavity, Yarm 85–100 ppm

Arm cavity build–up, Garm 270

Power recycling gain, Gprc 38

Signal recycling attenuation, 1/Gsrc 0.11

Common coupled cavity build–up, G+ 5000

Differential coupled cavity build–up, G− 31.4

Common coupled cavity pole, f+ 0.6 Hz

Differential coupled cavity pole, f− 335–390 Hz

RF modulation index 0.13–0.26 rad

Test mass diameter 34 cm

Test mass thickness 20 cm

Beam size at end test mass 6.2 cm

Beam size at input test mass 5.3 cm

Mass of the test mass, M 40 kg

Several critical improvements distinguish AdvancedLIGO from the initial detectors [15]. The much im-proved seismic isolation system [23] reduces the impactof ground vibrations. All photodetectors, used in the ob-serving mode, are installed in vacuum to avoid the cou-pling of ambient acoustic noise to the gravitational wavechannel. The larger and heavier test masses lead to areduction of quantum radiation pressure induced motionand thermal noise [24]. Multi-stage pendulums with amonolithic lower suspension stage [25] filter ground mo-tion and improve suspension thermal noise. Furthermore,instead of using coil-magnet actuation pairs to exert con-trol forces on the test masses, electrostatic interaction isemployed. This actuation scheme helps to avoid cou-pling of magnetic noise to the gravitational wave chan-nel [26, 27].

Lower arm cavity loss, coupled with an increase in theavailable power from the Nd:YAG laser, allows up to800 kW of laser power to circulate in the arm cavities—20 times higher than in initial LIGO − significantly re-ducing the high frequency quantum noise. The use ofoptically stable folded recycling cavities allows for bet-ter confinement of the spatial eigenmodes of the opticalcavities [28]. The signal recycling cavity [29], which wasnot present in initial LIGO, was introduced at the anti-symmetric port to broaden the frequency response of thedetector and improve its sensitivity at frequencies below

5

80 Hz and above 200 Hz.Because O1 was the first observing run, and work re-

mains to be done on the detectors to bring them to theirdesign sensitivity, not all of the interferometer param-eters were at their design values during O1. Most no-tably, the laser power resonating in the arm cavities was100 kW instead of the planned 800 kW. More power in thearm cavities improves the shot noise level as discussed inSec. III B. Circulating optical power will be increased infuture observational runs. Additionally, the signal recy-cling mirror transmissivity was 36%, in contrast to thedesign value of 20%. This higher transmissivity of thesignal recycling mirror improves the quantum noise inthe frequency range from 60 Hz to 600 Hz at the priceof reducing the sensitivity at other frequencies. Finally,the best measured Advanced LIGO sensitivity in the fre-quency range 20–100 Hz, as discussed in Sec. III, is lim-ited by a wide range of understood technical noise sourcesas well as currently unknown noise sources.

Fig. 2 shows the Advanced LIGO detector’s sensitivityduring the first observing run. The performance of boththe L1 and H1 detectors is compared to the initial LIGOsensitivity and the design sensitivity: the improvementwith respect to S6 was 3–4 times at 100 Hz and higherfrequencies. Below 100 Hz, the upgraded seismic isola-tion system yielded even larger improvements, with morethan an order-of-magnitude-better strain sensitivity forfrequencies below 60 Hz. The sensitivity of AdvancedLIGO can also be quantified as maximum distance atwhich a given astrophysical source would be detectable,known as “horizon distance”. Fig. 3 shows the horizondistance as a function of the chirp mass for coalescenceof neutron star (M <∼ 2M) and black hole (M >∼ 2M)binaries. For chirp masses <∼ 100M horizon distanceincreases with chirp mass since gravitational wave signalis stronger from heavier binary systems. However, thesignal also shifts towards lower frequencies (and out ofLIGO frequency band) for massive binary systems, andhorizon distance decreases for chirp masses >∼ 100M.

A. Interferometer Controls

In operation the laser light needs to resonate insidethe optical cavities. This requires that the residual lon-gitudinal motion of the optical cavities be kept withina small fraction of the laser wavelength [30]. The sus-pended mirrors naturally move by ∼ 1µm at the micro-seismic frequencies around 100 mHz—much larger thanthe width of a resonance. To suppress this motion, asophisticated length sensing and control system is em-ployed, using both the well-known Pound-Drever-Halltechnique [31, 32] and a version of homodyne detectionknown as “DC readout” [33]. Table II shows linewidthsand requirements for residual root-mean-square (RMS)motion of the main interferometric degrees of freedom.

An electro-optic modulator generates radio frequency(RF) phase modulation sidebands at 9 MHz and 45 MHz,

TABLE II. The linewidths of Pound-Drever-Hall signals andthe requirements for residual RMS motion for the main inter-ferometric degrees of freedom.

Degree of freedom Linewidth Residual

Common arm length 6 pm 1 fm

Differential arm length 300 pm 10 fm

Power recycling cavity length 1 nm 1 pm

Michelson length 8 nm 3 pm

Signal recycling cavity length 30 nm 10 pm

symmetrically spaced about the laser carrier frequency.The Pound-Drever-Hall technique is used to sense all lon-gitudinal degrees of freedom except for the differentialarm channel. Feedback control signals actuate on thesuspended mirrors, using either coil-magnet or electro-static actuation. The common arm cavity length is alsoused as a reference to stabilize the laser frequency, withsub-mHz residual fluctuations (in detection band).

The gravitational wave signal is extracted at the anti-symmetric port of the interferometer, where fluctuationsin the differential arm cavity length are sensed. The armcavities are held slightly off-resonance by an amount re-ferred to as the differential arm offset ∆L. This offset ofroughly 10 pm generates the local oscillator field, whichis necessary for the DC readout. An output mode cleaner[34] located between the antisymmetric output and thehomodyne readout detectors, is used to filter out the RFsidebands as well as any higher-order optical modes, asthese components do not carry information about thedifferential arm cavity length.

A similar feedback control scheme is employed to keepthe optical axes aligned relative to each other and thelaser beam centered on the mirrors [35]. This systemis required to maximize the optical power in the reso-nant cavities and keep it stable during data collection.A set of optical wavefront sensors is used to sense inter-nal misalignments [36]. At the same time, DC quadrantphotodetectors sense beam positions relative to a globalreference frame. The test mass angular motions are sta-bilized to 3 nrad rms, keeping power fluctuations in thearm cavities smaller than 1% on the time scale of a fewhours.

B. Strain Calibration

For the astrophysical analyses, the homodyne readoutof the differential arm cavity length needs to be calibratedinto dimensionless units of strain [37]. This is compli-cated by the fact that the feedback servo for this degree-of-freedom has a bandwidth of about 100 Hz, extendingwell into the band of interest. Denoting the control signalsent to the end test masses with s, and the error signal,as measured by the photodiodes in units of W, with e,

6

FIG. 4. Time-varying response of the Advanced LIGO de-tectors. The top panel shows the optical gain variations overa time span of one month, whereas the bottom panel showsthe variations of the differential coupled cavity pole frequencyover the same time span. The blue traces are for the LIGOLivingston Observatory (L1) and the red traces for the LIGOHanford Observatory (H1).

the strain signal h is

h = As+ C−1e, (5)

where A is the calibration of the actuator strength intostrain and is computed using dynamical models. Transferfunction C is the optical response from strain to the errorsignal and is given by

C(f) =4πGarmL0

λ

(GprcPinPLO

Gsrc

)1/2

K−(f), (6)

where Pin is the interferometer input power and PLO ispower of the local oscillator coming out from the interfer-ometer. Signal recycling cavity gain Gsrc = 9.2 is in thedenominator since differential arm signal is anti resonantin this cavity.

Ideally, the actuator transfer function A is stable overtime. In practice, a time-varying charge accumulates onthe test masses, changing the actuation strength and in-troducing noise into the gravitational wave channel (seeSec. III D). The optical transfer function C is also non-stationary, being modulated mainly by angular motionof the test masses.

The optical response C is tracked using a systemknown as the “photon calibrator”, which consists of anauxiliary Nd3+: YLF laser (operating at a wavelength of1047 nm), an acousto-optic modulator, and a set of inte-grating spheres [38]. This calibration system actuates onthe end test masses, applying set of sinusoidal excitationsvia radiation pressure, to track variations of the opticalgain and of the differential coupled cavity pole frequency.Three weeks of such data are shown in Fig. 4, showingthat the optical response of the detectors is stable overtime.

The absolute accuracy of the photon calibrator is lim-ited by the uncertainties in its photodetector calibration,

as well as any optical losses between the test mass andthe photodetector. Overall, the uncertainty in the cali-bration of the interferometer over the entire operationalfrequency range from 10 Hz−5 kHz is estimated to besmaller than 10% and 10 degrees [39].

III. ANALYSIS OF THE INSTRUMENTALNOISE

The calibrated gravitational wave signal is comparedto the known noises in order to understand what lim-its the sensitivity of the instrument as a function of fre-quency. Fig. 5 summarizes the noise contributions fromvarious sources to the gravitational wave channel for theLivingston and Hanford detectors. The coupling of eachnoise source to the gravitational wave channel at a fre-quency f is estimated using the following equation:

L(f) = L0h(f) = T (f)×N(f), (7)

where N(f) is the noise spectrum measured by an auxil-iary (witness) sensor or computed using analytical model,and T (f) is the measured or simulated transfer functionfrom this sensor to the gravitational wave channel.

Noise sources can be divided into classes according totheir origins and coupling mechanisms [40? ]. One clearway to differentiate noises is to split them into displace-ment and sensing noises: displacement noises cause realmotion of the test masses or their surfaces, while sensingnoises limit the ability of the instrument to measure testmass motion. However, this distinction is not perfect,since some noise sources (e.g., laser amplitude noise) canbe assigned to both categories, as discussed in Sec. III E.

Another way to classify noise sources is to divide theminto fundamental, technical and environmental noises.Fundamental noises can be computed from first princi-ples, and they determine the ultimate design sensitivityof the instrument. This class of noises, which includesthermal and quantum noise, cannot be reduced withouta major instrument upgrade, such as the installation ofa new laser or the fabrication of better optical coatings.Technical noises, on the other hand, arise from electron-ics, control loops, charging noise and other effects thatcan be reduced once identified and carefully studied. En-vironmental noises include seismic motion, acoustic andmagnetic noises. The design of Advanced LIGO calls forthe contributions of technical and environmental noisesto the gravitational wave channel to be small comparedto fundamental noises. In practice, the sensitivity canbe reduced due to unexpected noise couplings. Manytechnical and environmental noises have been identifiedand are discussed in the following sections. At the sametime, the dominant noise contributor in the frequencyrange 20–100 Hz has not yet been identified.

The narrowband features in the sensitivity plots shownin Fig. 5 are caused by power lines (60 Hz and harmonics),suspension mechanical resonances, and excitations thatare deliberately added to the instrument for calibration

7

101 102

Frequency, Hz

10-20

10-19

10-18

10-17

Dis

pla

cem

en

t, m

/Hz1/

2Measured noiseQuantum noiseDark noiseSeismic+NewtonianThermal noiseGas noiseMICH control

SRCL controlAngular controlsOutput jitterSuspension dampingSuspension actuationExpected noise

(a) LIGO Livingston Observatory

102 103

Frequency, Hz

10-21

10-20

10-19

10-18

Dis

pla

cem

en

t, m

/Hz1/

2

Measured noiseQuantum noiseDark noiseThermal noiseGas noise

Frequency noiseIntensity noiseInput jitterRF oscillator noiseExpected noise

(b) LIGO Hanford Observatory

FIG. 5. Noise budget plots for the gravitational wave channelsof the two LIGO detectors. The strain sensitivities are sim-ilar between the two sites. Plot (a) shows the low-frequencycurves for L1, whereas Plot (b) shows the high-frequencycurves for H1 detector. Quantum noise is the sum of thequantum radiation pressure noise and shot noise. Dark noiserefers to electronic noise in the signal chain with no light in-cident on the readout photodetectors. Thermal noise is thesum of suspension and coating thermal noises. Gas noise isthe sum of squeezed film damping and beam tube gas phasenoises. The coupling of the residual motion of the Michelson(MICH) and signal recycling cavity (SRCL) degrees of free-dom to gravitational wave channel is reduced by a feedforwardcancellation technique. At low frequencies, there is currentlya significant gap between the measured strain noise and theroot-square sum of investigated noises. At high frequencies,the sensitivity is limited by shot noise and input beam jitter.

and alignment purposes. These very narrow lines are eas-ily excluded from the data analysis, while the broadbandnoise inevitably limits the instrument sensitivity. Thelatter is therefore a more important topic of investiga-tion.

A. Seismic and thermal noises

Below 10 Hz, there is significant displacement noisefrom residual seismic motion. On average, at boththe Livingston and Hanford sites, the ground moves by∼ 10−9 m/

√Hz at 10 Hz—ten orders of magnitude larger

than the Advanced LIGO target sensitivity at this fre-quency. To address this difference, seismic noise is fil-tered using a combination of passive and active stages.The test masses are suspended from quadruple pendu-lums [25]. These passive filters have resonances as lowas 0.4 Hz and provide isolation as 1/f8 in the detectionbandwidth. The pendulums are mounted on multistageactive platforms [41, 42]. These systems use very-low-noise inertial sensors to provide the required isolationin the detection band and at lower frequencies (below10 Hz). This isolation is crucial for bringing the interfer-ometer into the linear regime and allowing the longitu-dinal control system to maintain it on resonance. Theactive platforms combine feedback and feedforward con-trol to provide one order of magnitude of isolation atthe microseism frequencies (around 0.1 Hz) and three or-ders of magnitude between 1 Hz and 10 Hz. Most of thesuspension resonances are located in this band, whereground excitation from anthropogenic noise and wind issignificant.

Fluctuations of local gravity fields around the testmasses—caused by ground motion and vibrations of thebuildings, chambers, and concrete floor—also couple tothe gravitational wave channel as force noise [43] (grav-ity gradient noise). The coupling to the differential armlength displacement is given by

L(f) = 2Ngrav(f)

(2πf)2

Ngrav(f) = βGρNsei(f),

(8)

where Ngrav is the fluctuation of the local gravity fieldprojected on the arm cavity axis, the factor of 2 ac-counts for the incoherent sum of noises from the four testmasses, G is the gravitational constant, ρ ' 1800 kg m−3

is the ground density near the mirror, β ' 10 is a geo-metric factor, and Nsei is the seismic motion near thetest mass. Since the ground near the test masses movesby ' 10−9m/

√Hz at 10 Hz, local gravity fluctuations at

this frequency are Ngrav ≈ 10−15m s−2/√

Hz and the to-tal noise coupled into the gravitational wave channel at10 Hz is L ≈ 5× 10−19 m/

√Hz. Gravity gradient noise is

one of the limiting noise sources of the Advanced LIGOdesign in the frequency range 10–20 Hz. However, thetypical sensitivity measured during O1 is still far fromthis limitation.

Thermal noises arise from finite losses present in me-chanical systems and couple to the gravitational wavechannel as displacement noises. Several sources of ther-mal noise can be identified. Suspension thermal noise [45]causes motion of the test masses due to thermal vibra-tions of the suspension fibers. Coating Brownian noise

8

is caused by thermal fluctuations of the optical coatings,multilayers of silica and titania-doped tantala [47–50].Thickness of the coatings was optimized to reduce theirthermal noise and provide the required high reflectiv-ity of the mirrors [51, 52]. Thermal noise also arises inthe substrates of the test masses [53, 54], but this effectis less significant. Thermal noise levels are analyticallycomputed using the fluctuation-dissipation theorem [55]and independent measurements of the losses of materi-als. The model predicts that thermal noise limits theAdvanced LIGO design sensitivity in the frequency band10–500 Hz, but is below current sensitivity by a factor of≥ 3.

B. Quantum noise

Quantum noise is driven by fluctuations of the opti-cal vacuum field entering the interferometer through theantisymmetric port [56, 57]. This fundamental noise cou-ples to the interferometer sensitivity in two complemen-tary ways [58]. For one, vacuum fluctuations disturb theoptical fields resonating in the arm cavities, creating dis-placement noise by exerting a fluctuating radiation pres-sure force that physically moves the test masses [59, 60].The vacuum field is amplified by the optical cavities, andthe noise seen in the differential arm channel is given by:

L(f) =2

cMπ2f2(hνG−Parm)

1/2K−(f)

L(f) =1.38× 10−17

f2

(Parm

100 kW

)1/2

K−(f)m√Hz

,

(9)

where h is Planck constant and Parm is the power cir-culating in the arm cavities. This “quantum radiationpressure noise” imposes a fundamental limit to the de-sign sensitivity below 40 Hz, though it is still far frombeing a concern at the present operating power [24].

The vacuum fluctuations entering interferometerthrough the antisymmetric port also introduce shot noisein the gravitational wave channel [61]. Vacuum fluctua-tions also mix with the main beam due to optical lossesbetween the interferometer and the photodetector. Inthe current state of Advanced LIGO 25% of power atthe antisymmetric port is lost due to the output Faradayisolator, mode mis-match of the beam into the outputmode cleaner cavity, and imperfect quantum efficienciesof the photodetectors. So the fraction of the power thatis transmitted to the photodiodes is η = 0.75.

Differential arm sensing noise due to shot noise on thephotodetectors can be written as L(f) = L0Nshot/C(f)η,where Nshot = (2hνηPLO)1/2 is the shot noise on the

photodetector in units of W/√

Hz. The signal transferfunction C(f) is determined by Eq. 6. The total shot

noise is given by equations

L(f) =λ

4πGarm

(2hνGsrc

GprcPinη

)1/21

K−(f)

L(f) = 2× 10−20(

100 kW

Parmη

)1/21

K−(f)

m√Hz

.

(10)

Local oscillator power PLO cancels out in the final equa-tion, and shot noise level is independent of the differentialarm offset for small offsets ∆L <∼ 100 pm.

The Advanced LIGO optical configuration is tuned tomaximize power circulating in the arm cavities. Com-mon coupled cavity build–up (ratio between the powerresonating in the arms and power entering the interfer-ometer) is related to the losses in the arm cavities by

Gcomm<∼

1

2Yarm, (11)

where Yarm is round trip optical loss in one arm. Dur-ing O1 the power circulating in the arm cavities wasGcomm ' 5000 greater than the power entering the in-terferometer, corresponding to a round trip optical lossof Yarm ' 100 ppm in each arm cavity. The target op-tical gain for Advanced LIGO was 7500, which corre-sponds to round trip losses in the arm cavities of about75 ppm. This number can possibly be achieved once thetest masses are replaced after the second science run.The discrepancy in the round trip losses between thepredicted and measured values is currently under study.Shot noise limits the design sensitivity above 40 Hz, andthe current sensitivity above 100 Hz.

C. Gas noise

The Advanced LIGO optics are located inside vacuumchambers. The gas pressure in the corner station, wherethe dual-recycled Michelson interferometer is housed, andin the 4-km arm tubes, is maintained below 10−6 Pa. Thepresence of residual gas causes both displacement andsensing noise: thermal motion of gas molecules inside thevacuum chambers results in momentum exchange withthe test masses via collisions; meanwhile, forward scat-tering of photons by the gas molecules in the arm tubesmodulates the optical phase of the beam.

1. Squeezed film damping

Residual gas in the vacuum system exerts a damp-ing force on the test masses and introduces displacementnoise [62]. This noise is amplified by a factor of ∼10 be-low 100 Hz due to the small gap of 5 mm between the endtest and reaction masses [63] (the top view of a test massand its surroundings is shown in Fig. 7). The total noisecan be estimated by applying the fluctuation-dissipationtheorem or by running a Monte Carlo simulation [64].

9

The coupling coefficient depends on the gas pressure andthe molecular mass, and it is found to be (below 100 Hz)

F (f) = 1.5× 10−14( p

10−6

)1/2( m

mH2

)1/4N√Hz

, (12)

where p is the residual gas pressure in Pa, and m is themass of a gas molecule. The calculated squeezed filmdamping noise shown in Fig. 5 (a) is the sum of con-tributions from nitrogen (pN2

≈ 6 × 10−7 Pa), hydrogen(pH2

≈ 2× 10−6 Pa) and water (pH2O ≈ 10−7 Pa).

100 300 600 1000 2000Frequency, Hz

10-20

10-19

Dis

plac

emen

t, m

/Hz1/

2

Total noise at 10uPaTotal noise at 6uPaQuantum noiseTotal classical noise at 10uPaTotal classical noise at 6uPaEstimated gas noise at 10uPaEstimated gas noise at 6uPaOther classical noises

FIG. 6. Measurement of the gas phase noise for the two dif-ferent pressures (average values are 10 uPa and 6 uPa) in one4 km arm of the Livingston detector. The red and blue tracesshow total measured noise before and after the pump down.The dashed black curve shows the quantum noise level, whichis independent of the pressure in the arms. The green and or-ange curves show total classical noise at pressure 10 uPa and6 uPa correspondingly. The magenta and violet curves showthe estimated gas phase noises. Reduction of classical noiseis in agreement with the model that was used to computegas phase noise. The gray curve shows other classical noiseswhich do not depend on the gas pressure. Below 300 Hz thereis an unknown 1/f noise. At higher frequencies, classical noisegrows with frequency, and is dominated by dark noise of thephotodetectors and laser frequency noise.

2. Phase noise

Phase noise induced by the stochastic transit ofmolecules through the laser beam in the arm cavities,can be modeled by calculating the impulsive disturbanceto the phase of the laser field as a gas molecule movesthrough the beam [65]. Such a model was used to esti-mate the high frequency part of gas noise curve shownin Fig. 5 (b). This estimation accounts for the pressuredistribution in the arm cavities along with the profile ofthe laser beam, with the most significant noise contri-bution coming from the geometrical center of the tube,

where the beam waist is located. The expected noisefrom residual gas is given by

L(f) = 4× 10−21Ngasm√Hz

Ngas =

(agasaH2

)(mgas

mH2

)1/4 ( p

10−8

)1/2,

(13)

where agas is the polarization of the gas molecules.The estimation of the gas phase noise was verified by

changing the pressure in one of the arms by a factor of3 at the end station and factor of 1.7 at the half-waypoint. A variation of differential arm noise was measuredusing relative intensity fluctuations at the output port, asshown in Fig. 6. Though, as discussed in Sec. III B, thesensitivity above 100 Hz is limited by shot noise, classicalnoise can be revealed by incoherent subtraction of shotnoise from the measured signal. Using this technique,classical noise was observed to change during this test aspredicted by the model.

D. Charging noise

During the Advanced LIGO commissioning, it wasdiscovered that the electrostatic actuation on the testmasses was not symmetric among the four electrodes lo-cated on the reaction mass (see Fig. 7). This mismatch inactuation strength is caused by electrostatic charge [66],which is distributed on the test masses in a non-uniformmanner and is time dependent.

Ideally, there should be no charge on the test masses,except for the one accumulated due to electrostatic ac-tuation. However, some electric charge may be left byimperfect removal of the First Contact polymer used forcleaning and protection of the optics [67]. Moreover, sur-faces of the test masses also lose electrons due to UVphotons, generated by nearby ion pumps used in the vac-uum system. Dust particles in the vacuum system pro-vide yet another source of charging. It was discoveredthat the charge distribution changes on the week timescale. An order-of-magnitude estimate of the charge den-sity on the front and back surfaces of the end test massesis σ ∼ 10−11 C/cm2. This number was achieved by ex-citing the electrodes and the potential of the ring heaterswhile measuring the longitudinal and angular motion ofthe test mass.

There are two coupling mechanisms of charging noiseto the gravitational wave channel. The first mechanismarises due to interaction of the time – variant charge withthe metal cage around the test mass. The second cou-pling mechanism comes from voltage fluctuations of thevarious pieces of grounded metal in the vicinity of thetest mass. Voltage noise creates fluctuations of the elec-tric field E and applies a force Fch on the test mass ac-cording to the following equation

Fch =

∫EσdS, (14)

10

Reactionmass

Electrodes

Ringheater

Suspensioncage

HRcoating

Testmass

FIG. 7. Top and front views of a test mass showing the ar-rangement of the electrodes, high reflective (HR) coating, ringheater and surrounding metal cage. Electrodes are used foractuation on the test mass. The ring heater is used to correctthe curvature of the mirror.

where the integral is computed over both the front andback surfaces of the test mass. In this paper, we consideronly the second coupling mechanism, since it is estimatedto be the dominant one.

The broadband voltage noise on the ground plane ismeasured to be roughly 1 uV/

√Hz. This number was

measured between the grounded suspension cage and thefloating ring heaters. Since the characteristic distancebetween the test masses and the metal cage is 10 cm, thefluctuations in the electric field near the test mass are∼ 10−5 V/m/

√Hz. The total noise coupling above 10 Hz

is estimated using the equation

L(f) =Fch

M(2πf)2≈ 10−16

f2σ

10−11C/cm2

m√Hz

. (15)

The coupling of voltage fluctuations on the groundplane to the gravitational wave signal was reduced by afactor of 10–100 by discharging the test masses. Chargefrom the front surface can be efficiently removed using ionguns [68, 69]: positive and negative ions are introducedinto the chamber, when the pressure inside is ∼ 103 Pa,and annihilate surface charges on the front surface of thetest mass. During the discharge procedure, it was foundthat the ions cannot efficiently reach the back surfacedue to the small gap between the test mass and the re-action mass, as shown in Fig. 7. The back surface of theend test masses was discharged by opening the chambers,separating the test and reaction mass, and directing anion gun at close range towards the surfaces in the gap.

E. Laser amplitude and frequency noise

Advanced LIGO employs a Nd:YAG nonplanar ringoscillator as the main laser [19]. Intensity and frequencyfluctuations of such a laser can be roughly approximatedas 10−4/f /

√Hz and 104/f Hz/

√Hz, respectively, in the

frequency range 10 Hz−5 kHz. In the same band, theAdvanced LIGO requirements are ∼ 10−8 /

√Hz for in-

tensity noise and ∼ 10−6 Hz/√

Hz for frequency noise.In order to meet those requirements, a hierarchical con-trol system is implemented. First of all, laser noises areactively suppressed using intensity and frequency stabi-

lization servos. Additionally, laser noise on the beam en-tering the main interferometer is passively filtered by K+

(Eq. 4) due to the common-mode coupled cavity pole.For laser amplitude noise, there are several coupling

mechanisms. First of all, the presence of the nonzero dif-ferential arm offset4L needed for the homodyne readoutmeans that the carrier light at the antisymmetric port isdirectly modulated by amplitude noise entering the in-terferometer. In addition, mismatches in the circulatingarm powers and in the mirror masses also lead to inten-sity noise coupling through radiation pressure force atlow frequencies (below 50 Hz).

100 300 600 1000 2000Frequency, Hz

-60

-55

-50

-45

-40

-35

-30

Mag

nitu

de, d

B

FIG. 8. Measured transfer function of intensity fluctuationsfrom interferometer input to the antisymmetric port. Theblue trace corresponds to the case when substrate lenses ofinput test masses are matched. The red trace shows the cou-pling when substrate lenses are different by 7.5µD. For thedifference of 40µD the coupling above 60 Hz increases up to-25 dB.

Above 100 Hz, the most significant broadband couplingof laser amplitude noise comes from unequal effectivelenses in the input test masses, due to substrate inho-mogeneity. The presence of imbalanced lenses createsa direct conversion of the fundamental laser mode intohigher-order spatial modes. As these modes do not res-onate in the arm cavities, they are not filtered by thecommon-mode coupled cavity, and they therefore con-tribute to the coupling of laser intensity noise with aflat transfer function. A thermal compensation system(TCS) [70], which employs auxiliary CO2 laser beamsand ring-shaped heating elements, has been installed tocompensate for such imbalances. Fig. 8 shows that thecoupling of intensity noise can be significantly reducedby equalizing the substrate lenses using the TCS system:if no correction is applied, the differential lens poweris 40µD and the coupling coefficient at 300 Hz is morethan 40 dB larger than the lowest value attainable witha proper TCS correction.

Laser frequency noise is largely cancelled at the anti-symmetric port by virtue of the Michelson interferome-ter common-mode rejection (∼ 1000 at 100 Hz). How-ever, residual frequency noise couples into the gravita-tional wave channel through the intentional asymmetrythat is introduced into the Michelson interferometer to

11

produce the necessary interference conditions for the RFcontrol sidebands, and through imbalances in arm cavityreflectivities and pole frequencies [71, 72]. The achievedlaser frequency noise performance is limited primarily bysensing noises (shot noise, photodiode noise, and elec-tronics noise) in the feedback control that stabilizes thelaser frequency to the interferometer’s common (mean)arm length. In Advanced LIGO, noise in the frequencystabilization error signals limits the residual frequencynoise of the beam entering the main interferometer to' 10−6 Hz/

√Hz between 10 and 100 Hz, and increasing

as f above 100 Hz.

F. Auxiliary Degrees-of-Freedom

The use of a dual-recycled Michelson interferometeroptimizes the detector response to gravitational waves.Additionally, active control of the mirror angular degreesof freedom is important to stabilize the interferometer op-tical response. However, any noise in the associated aux-iliary degrees of freedom will couple to the gravitationalwave channel at some level. Fig. 9 shows the typicalnoise in the auxiliary longitudinal degrees of freedom cal-ibrated into displacement, as well as the typical angularnoise in one of the arm cavity pitch degrees of freedom.

Any residual fluctuation of the Michelson length Nmich

couples to the transmitted power of the output modecleaner, where the gravitational wave channel is trans-duced. The coupling mechanism is similar to that of adifferential arm length fluctuation, but without the am-plification factor provided by the arm cavity build-upGarm = 270:

L(f) =1

GarmNmich(f). (16)

This coupling coefficient depends only weakly on thedifferential arm offset and alignment, unless the powerbuild-up in the arm cavities is significantly changed.

Residual fluctuations of the signal recycling cavitylength also couple to the gravitational wave channel, dueto the differential arm offset ∆L, through a radiationpressure force exerted on the test masses by the res-onating optical fields. In the frequency range from 10to 70 Hz, the differential arm noise L(f) due to signalrecycling cavity longitudinal noise Nsrcl can be modeledas

L(f) =0.16

f2∆L

10 pmNsrcl(f), (17)

where the numerical factor is determined mainly by thesignal recycling mirror reflectivity and the masses of thecavity mirrors. Besides this linear coupling, a non-linearcomponent appears due to low-frequency modulation ofthe differential arm offset ∆L (by ' 10 − 20%), whicharises from unsuppressed angular motion of the inter-ferometer mirrors. Such motion generates higher-order

mode content in the beam exiting the interferometerthrough the antisymmeteric port, leading to modulationof the power transmitted by the output mode cleaner andforcing the differential arm length servo to compensateby changing the offset ∆L. At higher frequencies (above70 Hz), the coupling of the signal recycling cavity longi-tudinal noise depends on the mode matching between thesignal recycling cavity and the arm cavities. This can betuned using the thermal compensation system discussedabove.

The coupling of the power recycling cavity length tothe differential arm channel is caused by imbalances inthe two arm cavities and cross couplings with other lon-gitudinal degrees of freedom. Residual power recyclingcavity length noise is less significant (by a factor of ≥ 10)compared to other degrees of freedom of the dual-recycledMichelson interferometer.

Finally, any residual angular motion of the test massesNang couples to the gravitational wave channel geomet-rically due to beam mis-centering d on the mirrors, ac-cording to the equation

L(f) = d×Nang(f). (18)

The beam mis-centering itself is also modulated by themirror angular motion d = d + dac, where d and dac ∝Nang are stationary and non-stationary components ofthe beam position. For this reason, the coupling of theangular motion can be linear and non-linear. The angularfeedback servos are optimized to suppress low-frequencymotion of the cavity axis and dac while avoiding injectionof sensor noise at high frequencies.

The linear coupling of the auxiliary degrees of freedomto the gravitational wave channel is mitigated using a re-altime feed-forward cancellation technique. Witness sig-nals are properly reshaped using time-domain filters, andthe cancellation signals are applied directly to the testmasses. This feed-forward scheme significantly reducesthe contribution of noise in auxiliary degrees of freedomto the gravitational wave channel in the frequency range10–150 Hz. The typical subtraction factors for Michelsonlength noise, signal recycling cavity length noise, and an-gular noise are 30, 7 and 20, respectively.

G. Oscillator noise

The RF oscillator used to generate the Pound-Drever-Hall control sidebands has phase and amplitude noise,and these couple to the gravitational wave channel viaboth sensing intensity noise and displacement noise inthe dual-recycled Michelson degrees of freedom.

Noise in the oscillator amplitude causes the RF modu-lation index to vary with time, thus changing the amountof power contained in the RF sidebands. Since the to-tal power in the carrier and the RF sidebands is activelycontrolled, fluctuations in the RF sideband field ampli-tudes produce fluctuations in the carrier field amplitude(i.e., audio sidebands). These audio sidebands propagate

12

101 102 103

Frequency, Hz

10-18

10-17

10-16

10-15

10-14

10-13

10-12D

ispl

acem

ent,

m/H

z1/2

Measured noiseSeismic noiseSuspension dampingThermal noiseDark noiseQuantum noiseActuator noiseExpected noise

101 102 103

Frequency, Hz

10-18

10-17

10-16

10-15

10-14

10-13

10-12

Dis

plac

emen

t, m

/Hz1/

2

Measured noiseSeismic noiseSuspension dampingThermal noiseDark noiseQuantum noiseActuator noiseBeam splitter motionExpected noise

(a) Michelson length. (b) Power recycling cavity length.

101 102 103

Frequency, Hz

10-17

10-16

10-15

10-14

10-13

10-12

Dis

plac

emen

t, m

/Hz1/

2

Measured noiseSeismic noiseSuspension dampingThermal noiseDark noiseQuantum noiseActuator noiseBeam splitter motionExpected noise

Frequency, Hz10-2 10-1 100 101 102

Pitc

h, r

ad/H

z1/2

10-18

10-16

10-14

10-12

10-10

10-8

10-6

Residual motionRMS of residual motionControl signalRMS of control signal

(c) Signal recycling cavity length. (d) Test mass angular motion (pitch).

FIG. 9. Noise budgets for auxiliary degrees of freedom. Plot (a) shows the noise curves for the Michelson length, Plot (b) forthe power recycling cavity length, Plot (c) for the signal recycling cavity length, and Plot (d) for the angular motion of oneof the test masses in pitch. The signals are measured with the full interferometer operating in the linear regime. The mostsignificant noise sources in the dual-recycled Michelson degrees of freedom are seismic noise, shot noise and electronics noisein the interferometric readout chains and in local sensors on the individual suspensions. Quantum noise in the signal recyclingcavity length is signiticantly affected by the differential arm offset below 10 Hz. In addition to coupling to the gravitationalwave channel, auxiliary degrees of freedom also couple to each other. For example, beam splitter motion above 10 Hz is causedby the Michelson control loop and dominates the power and signal recycling cavity length fluctuations in the frequency range10-50 Hz.

through the interferometer and couple into the gravita-tional wave channel via the same mechanisms as laserintensity noise as discussed in Sec. III E. Additionally,as intensity noise of RF sidebands is not filtered by thecommon coupled cavity pole and the output mode cleanerhas a finite attenuation at the RF sideband frequencies(' 6 × 10−5 W/W for the 45 MHz sidebands), a smallamount of sideband power fluctuations appears directlyon the GW readout photodiodes. The oscillator ampli-

tude noise coupling for the 9 MHz and 45 MHz sidebandswas measured to be

L(f) =5× 10−22

(N9

amp

10−6

)1

K−(f)

m√Hz

L(f) =5× 10−21

(N45

amp

10−6

)1

K−(f)

m√Hz

,

(19)

13

where N9amp and N45

amp is the relative amplitude noise of

9 MHz and 45 MHz sidebands in units of 1/√

Hz.

Oscillator phase noise is converted to RF sideband am-plitude noise through any optical path length imbalancein the interferometer’s Michelson degree of freedom. Themain sources of imbalance are the intentional asymme-try in the Michelson interferometer and a transmissivitydifference of the input test masses (which produces a dif-ferential phase delay when the sidebands are reflectedfrom each arm) [72]. The oscillator phase noise couplingfor the 9 MHz and 45 MHz sidebands was measured to be

L(f) =10−21

(N9

phf

10−2

)1

K−(f)

m√Hz

L(f) =10−22

(N45

phf

10−2

)1

K−(f)

m√Hz

,

(20)

where N9ph and N45

ph is the relative phase noise of 9 MHz

and 45 MHz sidebands in units of 1/√

Hz.

H. Beam jitter

Pointing fluctuations, quantified by the factor ∆w/w,where w is the beam size and ∆w is the transverse mo-tion of the beam, are also a source of noise. On the inputside, significant beam jitter is caused by angular and lon-gitudinal motion of the steering mirrors, located in air.The input mode cleaner, located in vacuum, attenuatesthe input beam jitter by a factor of ' 150. Fig. 10shows the relative pointing fluctuations before and afterthe input mode cleaner.

Residual input beam jitter is converted into intensityfluctuations by the interferometer resonant cavities: thepower and signal recycling cavities, the arm cavities, andfinally the output mode cleaner cavity. In the frequencyrange 100 Hz–1 kHz, the coupling coefficient from relativepointing noise at the interferometer input to the relativeintensity noise at the antisymmetric port is ∼ 0.01.

Fig. 5 shows that the contribution of the beam jitter isclose to the measured strain noise at a few peaks between200 and 600 Hz. These structures in the noise are due toresonances of mirror mounts in the in-air input beampath. This contribution has been reduced by improvingthe stiffness of the optical elements, thus reducing themotion.

On the output side, beam jitter is caused by angularmotion of the output steering mirrors. These are sin-gle pendulum stage suspended optics, located in vacuum.While interferometer alignment is actively controlled toreduce beam jitter, any residual angular motion modu-lates the power transmitted by the output mode cleanerand thereby couples to the gravitational wave channel.

50 100 200 500Frequency, Hz

10-9

10-8

10-7

10-6

10-5

10-4

Am

plitu

de, 1

/Hz1/

2

FIG. 10. Relative pointing noise before and after the inputmode cleaner in L1 interferometer. Acoustic peaks in the L1and H1 interferometers are at slightly different frequencies.The red trace shows the spectrum measured before the inputmode cleaner, where laser beam enters the vacuum system.The blue trace shows the measured jitter after the input modecleaner. This measurement is limited by the sensing noise ofthe quadrant photodetector at a level of 4× 10−8 /

√Hz. The

green trace is the estimated relative pointing noise used inthe calculation of the jitter coupling to the gravitational wavechannel. This curve is computed by dividing the red spectrumby the filtering coefficient of the input mode cleaner.

I. Scattered light noise

Motion of the suspended optics is significantly reducedcompared to the ground, as discussed in Sec. III A. How-ever, the vacuum chambers and arm tubes are not iso-lated from the ground seismic or the ambient acousticnoises. This motion can couple to the gravitational wavechannel through scattered light.

A small portion of the laser light scatters out of themain beam when it hits the optical components. Partof this light is scattered back from the moving cham-ber walls, baffles, mirrors, or photodiodes, and couplesinto the main beam as shown in Fig. 11. Backscatteredlight modulates the main beam in phase and amplitude,and introduces noise into the gravitational wave channel.The phase modulation is directly detected at the anti-symmetric port, and amplitude modulation moves thetest masses by means of radiation pressure. Signifiantscattering processes occur inside the arm cavities, at theinput and output ports, and in the recycling cavities.

1. Beam tubes

Light scattered out from the main beam by the testmasses couples motion of the 4–km beam tube to thegravitational wave channel. The bi-directional Reflec-tivity Distribution (BRDF) function of the test massesdepends on the imperfections in the mirror surface. If thewavelength of a coating ripple is λr, then the angle be-

14

Input test mass

4km

1m

End test mass

FIG. 11. Scattering inside the arm cavity. The test mass coat-ing irregularities and dust determines how much light can bescattered in and out from the main beam. After the scatteredlight hits the beam tube baffles, which are not isolated fromground motion or acoustic noise, it partially scatters back intothe main beam. This process couples motion of beam tubesto the gravitational wave channel.

tween the scattered light and the main beam is θ = λ/λr.The amount of power scattered out from the main beamdepends on the amplitude of the ripple. The fractionalpower scattered out in the cone with half angle θ 1and width dθ is given by:

dPsParm

≈(

4π

λ

)2

Sdθ

λ= BRDFm × dΩ (21)

where S(θ/λ) = S(λ−1r ) is the power spectral densityof the coating aberrations [74, 75], and dΩ = 2πθdθ issolid angle of scattering. For θ ∼ 1, the BRDF can beapproximated as BRDFm = 3× 10−6 cos(θ) sr−1.

Light scattered out from the main beam hits a baf-fle in the arm tube and scatters back into the mainbeam. The measured BRDF of the baffle at large an-gles is BRDFb = 0.02 sr−1. In order to get back into themain beam, light from the baffle scatters into the solidangle λ2/r2 ×BRDFm [76], where r is the distance fromthe baffle to the test mass. The total optical power Prthat recombines with the main beam is determined bythe following equation [77]:

dPrParm

=λ2

r2BRDF2

mBRDFbdΩ. (22)

The coating profiles were measured [24] and can be ap-proximated as a smooth polynomial function in the widerange of λr for narrow angle scattering. However, thehigh-reflectivity coatings applied on the end test massesshow a distinct azimuthal ripple in the coating surfaceheight. The spatial wavelength of the ripple is 7.85 mmand its maximum amplitude is 1 nm pk-pk. This rippleis located at radii beyond about 3 cm from the mirrorcenter and significantly contributes to the scattered lightnoise [78]. The total scattered light noise contribution tothe differential arm channel from the tube motion Ntubeis

L(f) =

√2

∫dPrParm

Ntube(f) ≈ 10−11Ntube(f), (23)

where the integral is computed over all scattering angles(the factor of 2 accounts for the incoherent sum of all four

test masses and for the fact that 1/2 of the baffle motion,in power, is in the phase quadrature of the main field).Equation 23 accounts only for the phase quadrature andignores radiation pressure noise. This is a valid assump-tion for the current optical power Parm ≈ 100 kW.

The estimated scattered light noise, coming from thearm cavities, is a factor of 30-100 below the current sen-sitivity of the interferometer. This result was confirmedby applying periodic mechanical excitation to the beamtube at different frequencies and measuring the responsein the gravitational wave channel.

2. Vacuum chambers

Similar scattering processes occur in the chambers andshort tubes in the corner station, where the dual-recycledMichelson interferometer is located. One method to as-sess the contribution of scattering noise to the detectorbackground is to inject known acoustic signals and mea-sure the response in the gravitational wave channel [79].In general, coupling of scattered light noise is not linearbut rather modulated by the low frequency motion of thescattering surfaces. For this reason, instead of measuringthe transfer function from the excitation to the sensor,we monitor excess power in the signal spectrum. Then wemake a projection of scattered light noise to the gravita-tional wave channel according to the following equation

L(f) = Namb(f)Lexc(f)

Nexc(f), (24)

where Lexc and Nexc are the spectra of the gravitationalwave channel and of the back scattering element motion,respectively, when an excitation to the element is applied,and Namb is the motion of the scattering element withoutany excitation. Fig. 12 shows that the projected ambientacoustic noise coupling to the gravitational wave channelis below the measured sensitivity.

3. Fringe wrapping

Scattered light may also manifest itself through up-conversion of the scattering element motion. One exam-ple of such a non-linear scattering process is fringe wrap-ping. In Advanced LIGO fringe wrapping occurs at theantisymmetric port of the interferometer. Optical imper-fections in the output mode cleaner cause a fraction ofthe light (∼ 1 ppm) to travel back into the interferometer.Most of this light is rejected by the output Faraday isola-tor, but a small fraction of scattered light gets through.Then this light is reflected from the instrument and trav-els back to the output mode cleaner, with an additionalvarying phase shift due to the relative motion of the out-put mode cleaner and the interferometer. The relativeintensity fluctuation (RIN) at the output mode cleanertransmission due to backscattering is given by [80]

RIN(t) = 2r cos(4πNomc(t)/λ), (25)

15

20 100 1000 5000Frequency, Hz

10-22

10-21

10-20

10-19

10-18D

ispl

acem

ent,

m/H

z1/2

GW signal channelEnd X bulidingEnd Y buildingCorner Station Center and Output AreaCorner Station Input AreaLaser Enclosure

FIG. 12. Projected contribution of the ambient acoustic noiseto the gravitational wave channel. An acoustic excitation wasapplied at different locations near the vacuum chambers: nearthe end test masses of both arm cavities (X and Y), near thedual-recycled Michelson interferometer (corner station), andnear the main laser.

where r = 10−5 − 10−4 is effective field reflectivity ofthe interferometer output port and Nomc(t) is the dis-tance fluctuation between the interferometer and theoutput mode cleaner. Since this distance is not con-trolled, the amplitude of Nomc(t) can be as large as sev-eral wavelengths, and the cosine in the above equationwraps this rapidly varying phase between 0 and 2π, lead-ing to up-conversion of the low frequency motion of thelength. The resulting “scattering shelves” are seen inthe differential arm length spectrum with a cutoff fre-quency of 2/λ × dNomc/dt. In Advanced LIGO, whenthe micro-seismic motion is higher than normal, this pro-cess increases the gravitational wave channel noise below20 Hz [73]. Fig. 13 shows scattering shelves in the gravita-tional wave channel during the low frequency modulationof the distance Nomc.

J. Sensing and actuation electronics noise

This section summarizes noise contributions from elec-tronic circuits in photodetectors, actuators, analog-to-digital (ADC) and digital-to-analog (DAC) convertersand whitening boards, all of which are essential for sens-ing optical signals and actuating on suspensions. From adesign perspective, all electronics noise should be smallerthan fundamental noises.

For the differential arm length signal, a pair of reverse-biased InGaAs photodiodes, equipped with in-vacuumpreamplifiers, measures the light transmitted by the out-put mode cleaner. Subsequently, these signals are ac-quired by a digital system through analog-to-digital con-verters, further dividing sensing noise into two types:dark noise and ADC noise. Dark noise includes any dark

101 102

Frequency, Hz

10-20

10-19

10-18

10-17

10-16

10-15

Dis

plac

emen

t, m

/Hz1/

2

FIG. 13. Scattering shelves in the differential arm channel.The red trace shows the spectrum when RMS of the groundvelocity is below ' 2 um/sec (usual conditions). The bluetrace shows the spectrum when the distance between the out-put mode cleaner and the interferometer was modulated atlow frequencies by ' 6 um/sec.

current produced by the photodiodes, Johnson-Nyquistnoise of the readout transimpedance, and noise in allother downstream analog electronics. A current noiselevel of ∼10 pA/

√Hz, at 100 Hz, is present in each pho-

todetection circuit, equivalent to the shot noise of a DCcurrent of 0.3 mA. This can be compared against the ac-tual operating current of 10 mA. Taking the coherent sumof two photodetectors into account, we estimate the darknoise to be a factor of 8.2 lower than the shot noise at100 Hz, as shown in Fig. 5. ADC input noise is sup-pressed by inserting additional analog gain and filtering,referred to as “whitening filters”. An offline measure-ment of the ADC noise shows that it is below the currentbest noise level by a factor of more than 10 over the entiremeasurement frequency band.

The other important noise in this category is noise inthe actuation used to apply feedback control forces onthe mirrors. Any excess noise at the level of the re-quired actuation couples directly to mirror displacement.The most critical actuation noise is due to the digital-to-analog convertors that bridge the digital real-time controlprocess and the analog suspension drive electronics. It isa significant challenge to achieve both the high-range ac-tuation, needed to bring the interferometer into the lin-ear regime from an uncontrolled state (lock acquisition)[30], and low-noise actuation for operation in the obser-vation state. This issue has been tackled by installing again-switchable force controller, which has several oper-ational states. After the interferometer is brought intothe linear regime, the controller state is changed from thehigh-dynamic-range to the low-noise state. Also, noisefrom the digital-to-analog converter is mechanically fil-tered via the suspension force-to-displacement transferfunction above ∼ 0.5 Hz. The current estimate puts theactuation noise is as low as 3× 10−18 m/

√Hz at 10 Hz.

Lastly, active damping of the suspension systems isknown to introduce noise. Below 5 Hz, the high-Q sus-

16

pension resonances are damped by sensing the motionof the suspension relative to its support using shadowsensors [26]. According to dynamical suspension mod-els, noise from the local damping control is estimated tobe 2 × 10−18 m/

√Hz at 10 Hz, and rapidly decreases at

higher frequencies.

K. Noise stationarity

FIG. 14. Sensitivity of the two Advanced LIGO detectorsto binary neutron star inspirals, averaged over sky positionand orientation and 1 minute of data. The sensitivity dropin the L1 interferometer at the end of the run was caused byelectronics noise at one of the end stations. This noise wasidentified and eliminated shortly after the observing run.

A common figure of merit for ground-based interfero-metric detectors is their sensitivity to the inspiral of twoneutron stars, averaged over relative orientations of thebinary system and sky locations. A plot of the sensitivityof the LIGO detectors to signals of this type is given inFig. 14, over a one-month timescale.

If the sum of all the noises is truly Gaussian and sta-tionary, the strain noise density at a given frequency willvary randomly in time following a Rayleigh distribution.In Fig. 15, we compare the 95th and 99.7th percentiles ofthe noise in each frequency bin to the expectation for sta-tionary Gaussian noise. Deviations from the expectationare due to non-stationary noises (e.g., transient environ-mental disturbances that generate very short-durationbursts of excess noise, mostly at low frequency) or nar-rowband features that are coherent over long timescales.Above 100 Hz, the deviation from stationary Gaussiannoise is small. Below 100 Hz, the fluctuations can maskor mimic gravitational waves and must be addressed byfurther commissioning and, for O1 data, through vetoesthat are applied following data collection and analysis.

The characterization and mitigation of the detectornoise is the focus of a large collaborative effort betweeninstrument specialists and the gravitational wave dataanalysis community [81, 82].

101 102 103

Frequency [Hz]

1

2

3

4

5

6

7

Stra

inA

SD,N

orm

aliz

edto

Med

ian H1 3σ

H1 2σL1 3σL1 2σGaussian Noise 3σGaussian Noise 2σ

FIG. 15. 95th (2σ) and 99.7th (3σ) percentiles of the noise ineach frequency bin during five days of operations (Oct 15-20).The expectations for stationary Gaussian noise at each per-centile are given by the colored dashed lines. Both detectorsexhibit some non-stationary behavior at low frequencies, dueto varying noise couplings with the environment.

IV. CONCLUSIONS

The first Advanced LIGO observational run (O1)started in September 2015 and concluded in January2016. The observatory was running at unprecedentedsensitivity to gravitational waves in the frequency range10 Hz–10 kHz. The average distance at which AdvancedLIGO could detect the coalescence of binary black holesystems with individual masses of 30M and with signal-to-noise ratio of 8 was 1.3 Gpc. The reach for binary neu-tron star inspirals during the first science run was about75 Mpc.

The commissioning of Advanced LIGO lasted for ∼ 1year before the beginning of O1. During this period, avariety of technical noise sources was discovered and elim-inated. In this paper, we discussed the dominant noisesources that limited Advanced LIGO sensitivity duringthe first science run. The coupling of auxiliary degreesof freedom, laser amplitude noise, suspension actuationand other technical noises considered in this paper weresignificantly reduced.

Future work is required to find the remaining noisesources. In particular, below 100 Hz, the sum of allknown noise sources in the gravitational wave channelcould not explain the measured sensitivity curve.

Above 100 Hz, the Advanced LIGO sensitivity was lim-ited mostly by photon shot noise. For this reason, onecertain activity on the commissioning agenda is to in-crease the interferometer input power and ultimately tointroduce squeezed states of light [61, 83, 84]. Duringthe first science run, Advanced LIGO operated in thelow power regime: input power was 25 W out of max-imum laser power of ' 180 W. A set of technical diffi-culties must be overcome before power can be increased.First of all, parametric instabilities [85], which arise athigh power, should be damped to keep the interferom-

17

eter in the linear regime. Second, angular instabilitiesin the arm cavities [86] are expected to occur when thecirculating arm power reaches ' 500 kW. This problemwill be addressed by changing the angular control systemcontrol topology. Lastly, power levels on the photodetec-tors should be adjusted in order to avoid their damageduring lock losses, when stored optical energy leaves theinterferometer through the output ports.

ACKNOWLEDGMENTS

The authors gratefully acknowledge the support of theUnited States National Science Foundation (NSF) forthe construction and operation of the LIGO Laboratoryand Advanced LIGO as well as the Science and Tech-nology Facilities Council (STFC) of the United King-dom, the Max-Planck-Society (MPS), and the State ofNiedersachsen/Germany for support of the constructionof Advanced LIGO and construction and operation ofthe GEO600 detector. Additional support for AdvancedLIGO was provided by the Australian Research Council.The authors gratefully acknowledge the Italian IstitutoNazionale di Fisica Nucleare (INFN), the French CentreNational de la Recherche Scientifique (CNRS) and theFoundation for Fundamental Research on Matter sup-ported by the Netherlands Organisation for Scientific Re-

search, for the construction and operation of the Virgodetector and the creation and support of the EGO consor-tium. The authors also gratefully acknowledge researchsupport from these agencies as well as by the Council ofScientific and Industrial Research of India, Departmentof Science and Technology, India, Science & Engineer-ing Research Board (SERB), India, Ministry of HumanResource Development, India, the Spanish Ministerio deEconomıa y Competitividad, the Conselleria d’Economiai Competitivitat and Conselleria d’Educacio, Cultura iUniversitats of the Govern de les Illes Balears, the Na-tional Science Centre of Poland, the European Commis-sion, the Royal Society, the Scottish Funding Council,the Scottish Universities Physics Alliance, the Hungar-ian Scientific Research Fund (OTKA), the Lyon Insti-tute of Origins (LIO), the National Research Foundationof Korea, Industry Canada and the Province of Ontariothrough the Ministry of Economic Development and In-novation, the Natural Science and Engineering ResearchCouncil Canada, Canadian Institute for Advanced Re-search, the Brazilian Ministry of Science, Technology,and Innovation, Russian Foundation for Basic Research,the Leverhulme Trust, the Research Corporation, Min-istry of Science and Technology (MOST), Taiwan andthe Kavli Foundation. The authors gratefully acknowl-edge the support of the NSF, STFC, MPS, INFN, CNRSand the State of Niedersachsen/Germany for provision ofcomputational resources.

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